Programmatically switching Flash apps to full screen mode in a browser is not allowed. Imagine what would happen if Flash apps on a site you browse to could go full screen without your permission.
One way you can approximate this behavior is to determine the size of the display inside your Flash app and then set your app to that size. For instance, in Strobe Media Player you might add something like:
However, this only set the size of the Flash app. You also have to define with size of the app when it is instantiated on a web page. Finally, you have to run a browser in kiosk mode so it will display the web page and nothing else. I've tested chrome kiosk mode in Linux and it works fine; cannot speak for Windows and OSX.
If your Flash player includes code such as the above example and you instantiate the .swf alone on an html page with a size of 1920x1200, for example, and you run the browser in kiosk mode, you will see your Flash app appear to be full screen on any display that is 1920x1200 or smaller.
This may or may not fit your application, but it is the best way I have found to approximate full screen programmatically.
I should have been more specific: this is a desktop-only application. It's actually a series of audio-visual classroom presentations for driver-training and I want all the presenter to control everything from the keyboard, so there are no buttons or cursors on the screen. I believe the OS will always be windows, and I don't think the Flash Player title bar or it's windows frame add anything to my graphics... the paying public should never "see the wires".
It seems that I'll have to publish for Adobe Air to get what I want without forcing the presenter to press Ctrl-F.